IDNStudy.com, kung saan ang iyong mga tanong ay natutugunan ng eksaktong sagot. Sumali sa aming platform upang makatanggap ng mabilis at eksaktong tugon mula sa mga propesyonal sa iba't ibang larangan.
Sagot :
To solve the quadratic equation 2x - 6 = 4x², we can follow these steps:
1. Subtract 2x from both sides:
2x - 6 - 2x = 4x² - 2x
-6 = 2x²
2. Divide both sides by 2:
-6/2 = 2x²/2
-3 = x²
3. Take the square root of both sides:
√(-3) = √(x²)
±√3i = x
Therefore, the solutions for x are:
x = ±√3i
The complex roots can be written in the form a + bi:
x = 1/4 (1 ± i√23)
The sum of the roots is:
1/4 (1 + i√23) + 1/4 (1 - i√23) = 1/2
The product of the roots is:
1/4 (1 + i√23) * 1/4 (1 - i√23) = 3/2
So, the solutions to the equation 2x - 6 = 4x² are:
x = 1/4 (1 - i√23)
x = 1/4 (1 + i√23)
where i is the imaginary unit (√(-1))[1].
I’m sorry to hear that you’ve been struggling with this quadratic equation! Let’s work through it together.
The given equation is: 2x−6=4x2
To find the value of (x), we can follow these steps:
1. Rearrange the equation to get all terms on one side:
[2x - 4x^2 - 6 = 0]
2. Combine like terms:
[4x^2 - 2x - 6 = 0]
3. Now, we can use the quadratic formula to find the solutions for (x):
[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}]
Here, (a = 4), (b = -2), and (c = -6).
Plugging in the values:
[x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \cdot 4 \cdot (-6)}}{2 \cdot 4}]
Calculating the discriminant:
[b^2 - 4ac = (-2)^2 - 4 \cdot 4 \cdot (-6) = 4 + 96 = 100]
Taking the square root of the discriminant:
[\sqrt{100} = 10]
Now we have two possible solutions:
[x_1 = \frac{-(-2) + 10}{8} = \frac{12}{8} = 1.5]
[x_2 = \frac{-(-2) - 10}{8} = \frac{-12}{8} = -1.5]
So the solutions for the equation are (x = 1.5) and (x = -1.5). Feel free to double-check the calculations, and let me know if you have any other questions!
and I hope you got rid of that math sick !
Salamat sa iyong kontribusyon. Huwag kalimutang bumalik upang magtanong at matuto ng mga bagong bagay. Ang iyong kaalaman ay mahalaga sa ating komunidad. Umaasa kami na natagpuan mo ang hinahanap mo sa IDNStudy.com. Bumalik ka para sa mas maraming solusyon!
